No-boundary measure in the regime of eternal inflation

James Hartle, S. W. Hawking, and Thomas Hertog
Phys. Rev. D 82, 063510 – Published 8 September 2010
An article within the collection: The Work of Stephen Hawking in Physical Review

Abstract

The no-boundary wave function (NBWF) specifies a measure for prediction in cosmology that selects inflationary histories and remains well behaved for spatially large or infinite universes. This paper explores the predictions of the NBWF for linear scalar fluctuations about homogeneous and isotropic backgrounds in models with a single scalar field moving in a quadratic potential. We treat both the spacetime geometry of the universe and the observers inhabiting it quantum mechanically. We evaluate top-down probabilities for local observations that are conditioned on the NBWF and on part of our data as observers of the universe. For models where the most probable histories do not have a regime of eternal inflation, the NBWF predicts homogeneity on large scales, a spectrum of observable fluctuations with a small non-Gaussian component, and a small amount of inflation in our past. By contrast, for models where the dominant histories have a regime of eternal inflation, the NBWF predicts significant inhomogeneity on scales much larger than the present horizon, a Gaussian spectrum of observable fluctuations, and a long period of inflation in our past. The absence or presence of non-Gaussianity in our observable universe therefore provides information about its global structure, assuming the NBWF.

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  • Received 15 January 2010

DOI:https://doi.org/10.1103/PhysRevD.82.063510

© 2010 The American Physical Society

Collections

This article appears in the following collection:

The Work of Stephen Hawking in Physical Review

To mark the passing of Stephen Hawking, we gathered together his 55 papers in Physical Review D and Physical Review Letters. They probe the edges of space and time, from "Black holes and thermodynamics” to "Wave function of the Universe."

Authors & Affiliations

James Hartle1, S. W. Hawking2, and Thomas Hertog3

  • 1Department of Physics, University of California, Santa Barbara, California 93106, USA
  • 2DAMTP, CMS, Wilberforce Road, CB3 0WA Cambridge, United Kingdom
  • 3APC, UMR 7164 (CNRS, Université Paris 7), 10 rue A. Domon et L. Duquet, 75205 Paris, France, and International Solvay Institutes, Boulevard du Triomphe, ULB-C.P. 231, 1050 Brussels, Belgium

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Issue

Vol. 82, Iss. 6 — 15 September 2010

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